The tracer zero-length column (ZLC) method has been employed to study the diffusion of toluene in one-dimensional ZSM-12 and SAPO-5 zeolites. A significant deviation in the shape of the measured tracer exchange curves from monoexponential behavior was observed for toluene diffusion in both adsorbents in the limit of long-time asymptotes. In contrast, water/ZSM-12 and acetylene/SAPO-5 systems exhibit tracer exchange curves that are close to monoexponential behavior. Monoexponential curves are usually observed for systems obeying normal (Fickian) diffusion. Such diffusion is expected for the latter two systems because the diameters of both sorbates are less than the radii of their corresponding host channels. The differences in the shape of the tracer exchange curves for large and small sorbates can be explained by assuming the occurrence of anomalous, single-file diffusion for large sorbates in narrow, one-dimensional channels.